1. Field of the Invention
This invention relates to the fabrication of high efficiency wavelength converters and their application in the field of nonlinear optical frequency conversion.
2. Description of the Related Art
Nonlinear frequency conversion provides a valuable tool for the generation of laser radiation in spectral ranges that are difficult if not impossible to obtain by conventional laser sources. Ferroelectric crystals (crystals having nonlinear polarizations) such as LiNbO3 or LiTaO3 or such crystals doped with MgO or ZnO are attractive candidates for use in such applications. Early attempts to use such crystals as a means for doubling the frequency of an incoming wave of optical radiation have shown that it is necessary to confine the incoming wave within an optical waveguide in order to maximize the conversion efficiency of the doubling process. Umegaki et al. (U.S. Pat. No. 4,820,011) form a waveguide by depositing nonlinear optical material between two glass substrates disposed facing each other. The frequency doubling conversion is produced by a Cherenkov type effect and at least one of the substrates is provided with a grating structure for permitting entry of the fundamental wave. The method of Umegaki is mentioned herein for purposes of historical completeness as the more recent approaches, particularly that of the present invention, produce frequency conversion within a ferroelectric crystal having disposed therein periodic regions of dipole moment domain inversion.
Since the frequency conversion method of the present invention, as well as related prior art methods, takes as a starting point a nonlinear ferroelectric crystal within which there has been formed a periodic configuration of domain reversed regions, a few words of explanation will be provided as to the properties of such a crystal. Ferroelectric materials have internal electric dipole moments which can be made to manifest themselves spontaneously on a macroscopic domain scale without the presence of external electric fields (hence the term “ferroelectric” by analogy with “ferromagnetic” for materials with domain scale magnetic dipole moments). These macroscopic polarizations are responsible for the optical properties of the materials through their effects on the propagation of electromagnetic radiation. When the polarization of such materials is linearly dependent (or only very weakly non-linearly dependent) on the electric field strength of an electromagnetic wave propagating through the material, the effect of the linear polarization is to produce a constant refractive index, which is responsible for modifying the speed of the wave through the material. In such a linear case, an incident oscillating electromagnetic field at frequency ω produces an oscillation of the polarization at the same frequency ω which, in turn, produces a re-radiated electromagnetic field also of the same frequency but out of phase with the incident wave.
The original incident wave, combined with phase-varying re-radiated waves along the forward propagation direction of the incident wave, creates a net transmitted wave that moves through the material at an apparently slower speed but same frequency. The speed, v(ω), of the transmitted wave in the crystal, is defined as c/n(ω), where c is the speed of the wave in vacuum (ie., the speed of light) and n(ω) is the index of refraction of the medium which, as indicated, depends on the frequency ω of the wave (ie., the medium is generally dispersive). Another important parameter of the medium is k(ω), the propagation constant of the radiation, which is defined as: k(ω)=2πn(ω)/λ, where λ is the wavelength of the wave in vacuum.
If the polarization at a position x within the crystal is a non-linear function of the field at that position, the propagation of an electromagnetic wave can be affected in additional ways. For example, the propagation of a wave with frequency ω1 will lead to the propagation of a secondary wave with frequency 2ω1, which is the second harmonic of the wave. If two waves, of different frequencies ω1 and ω2 simultaneously propagate through the non-linear crystal, there will be generated additional waves of frequencies ω1+ω2, ω1−ω2, 2ω1 and 2ω2. Each wave periodically modulates the polarization which the other wave sees and which it sees itself and, as a result, new waves are generated.
When waves at two different frequencies ω1 and ω2 and two different propagation constants k1 and k2 propagate a distance L through a non-linear crystal, one wave (k1) can transfer power to the other wave (k2) through the non-linearity of the polarization. The amount of power transferred after the wave has traveled a distance L in the crystal can be shown to be proportional to: L2(sin x/x)2, where x=(k3−k1−k2)L/2=LΔk/2 and k3 is the propagation constant of the polarization wave. If Δk is not zero, the transfer of power reaches a maximum value when the wave has propagated a distance called the coherence length, Lc, where LcΔk/2=π/2, ( ie. Lc=π/Δk). If Δk=0, the incident waves and the polarization wave are said to be phase locked and the power transfer increases along the entire length of the crystal and is proportional to L2, where L is the length of the entire crystal. If Δk is not zero, the maximum power transfer occurs within the coherence length, then goes to zero, then rises again in the next coherence length. In general, the power transfer within the coherence length is the maximum transfer possible, no matter through how many coherence lengths the waves propagate. Since obtaining a phase locked condition is very difficult in practice (it has been obtained using birefringent crystals) and will only occur at particular k values, an alternative approach to maximizing power transfer is through “quasi-phase matching” or QPM. QPM is obtained by changing the phase between the propagating wave and the polarization wave by π/2 every time the propagating wave moves through an additional coherence length. This can be accomplished by rotating the polarization direction within the crystal by 180° in successive coherence lengths. Unlike true phase matching, QPM can be obtained for a wave of arbitrary k value, providing the polarizations in the crystal can be rendered appropriately periodic in successive coherence lengths. Thus, by satisfying the QPM condition, the maximum power transfer is incremented in each successive passage of the wave through a coherence length, rather than falling to zero. Such a periodic rotation of polarization domains (domain reversals) of width Lc is usually accomplished by applying a high voltage to reverse the direction of the domain directly (of which more will be said in the following). Although quasi-phase matching does not produce the amount of power transfer produced by genuine phase matching (because the factor (sin x/x)2 is 1 for Δk=0, but is 4/π2 for LcΔk=π/2), it is much better than the non-QPM case. Much inventive effort has been expended in finding ways of rotating crystal polarizations in a periodic manner with the coherence length being the period.
A case of particular interest in modern technology occurs when ω2=2ω1, which is called frequency doubling or second harmonic generation (SHG). Obtaining a meaningful power transfer between an incident wave and its frequency doubled second harmonic allows the production, for example, of coherent green or blue light by the passage of near infra-red radiation from a solid state laser through a non-linear ferroelectric crystal. Since coherent infra-red radiation is easier to produce by laser action than coherent blue or green radiation, being able to obtain the green or blue by SHG is quite important. Such green or blue light is important for reading and writing optical storage disks. The coherence length needed to obtain efficient frequency doubling is given by: Lc=π/(2k1−k2). Note that 2k1−k2 is not zero because of the dispersion of the material, so true phase locking is generally not possible. As noted above, use of QPL by poling non-linear ferroelectric crystals such as congruent lithium niobate (congruent LiNbO3, or CLN) or stoichiometric lithium tantalate (stoichiometric LiTaO3 or SLT) allows frequency doubling of radiation within the entire range of frequencies for which these crystals are transparent: (0.32 microns–5.5 microns) for CLN and (0.27 microns–5.5 microns) for SLT.
Various approaches to form waveguides within non-linear optical materials to improve their conversion efficiency have been tried, including the diffusion of Ti, Zn and H+ ions. The key factors for high conversion efficiency are high non-linear response of the material, high optical power density for the interacting waves within the material, long interaction length for the waves and the maintenance of a good phasematching condition between the waves within the region of their interaction. As will be briefly discussed below, quasi-phasematching techniques have been developed to provide a good phasematching condition in certain nonlinear materials such as lithium niobate, lithium tantalate, potassium titanyl phosphate and strontium barium niobate, by the creation of a spatially periodic distribution of reversed ferroelectric domains of coherence length in which the orientation of the spontaneous polarization directions is reversed in adjacent domains. Although QPM improves the conversion efficiency of the crystal material, there is still a significant problem associated with the necessity of having the incident (pumping) radiation propagate in a tightly focused beam to provide adequate power density within the region of wave overlap. In bulk material, the pumping beam cannot be tightly focused since the propagation wave will diffract, therefore it is usually weakly focused, resulting in low conversion efficiency. A solution to this problem is to fabricate a waveguide configuration within the crystal, thereby maintaining a tightly confined beam over a long interaction length.
To achieve high conversion efficiency within a waveguide configuration it is necessary not only to tightly focus the beam to increase the optical power density, but also to increase the mode overlapping between the interaction waves (pumping wave and conversion wave) and the material nonlinearity (the polarization waves induced within the material). To accomplish this, the waveguide region of the material requires an optimized index of refraction profile which generally means both a high index and a symmetric profile. FIG. 1a is a schematic illustration of bad mode overlapping within a waveguide region having a poor index profile, whereas FIG. 1b is a schematic illustration of good mode overlapping within a waveguide configuration having an optimal index profile.
Several methods have been used in the prior art to fabricate waveguides on or within ferroelectric crystals. For example, a method to fabricate an annealed (heat treated) proton-exchanged waveguide has been tried, using pure benzoic acid to produce the exchange and a high temperature post heat treatment. Such methods lead to questionable results, particularly when doped ferroelectric materials are used. For example, Yamamoto et al. (U.S. Pat. No. 5,205,904) teach a method of forming an optical waveguide over a ferroelectric crystal which has been treated by proton exchange to form periodic domain inverted regions. The method comprises an initial formation of a titanium mask to protect the surface of the crystal during a heat treatment process applied after the proton exchange is carried out. The subsequent heat treatment allows the formation of deeper and more well-defined regions of domain inversion because the initial proton exchange is carried out below the Curie temperature of the crystal.
Also in this regard, Minakata et al. (U.S. Pat. No. 6,363,189 B1) teaches the formation of a directional coupler using at least two optical waveguides disposed within a ferroelectric crystal. The waveguides are formed by immersing a crystal that has been photolithographically patterned on its surface into benzoic acid at 200° C. for 30 minutes to form proton exchanged regions, then annealing the crystal at 300° C. for 4 hours to form the waveguide regions. This produces a difference of 4×10−3 between the indices of refraction of the crystal and the proton exchanged regions.
Mizuuchi et al. (U.S. Pat. No. 6,519,077 B1) adopts a two-step ion-exchange method to fabricate a waveguide with a high index cladding layer. The second ion-exchange is applied close to a surface region to which a first annealed ion-exchange has already been applied to form the cladding layer. The resulting two-step process produces a smooth but asymmetric index profile which does not allow optimal mode overlap as previously discussed.
Mizuuchi et al. (U.S. Pat. No. 5,872,884) also teaches a ridge type waveguide, which is a strip of high index of refraction material formed on the surface of a non-linear ferroelectric crystal together with a cladding layer that is formed over the strip. The indices of refraction are chosen so that the waveguide strip guides two wavelengths of light, λ1 and λ2, where λ1>λ2, while the cladding layer guides only λ2 and cuts off for λ1.
In an earlier patent, Yamamoto et al. (U.S. Pat. No. 4,946,240) also teach a ridge type waveguide disposed on the surface of a LiNbxTa1−xO3 substrate. The ridge, which is not cladded, propagates a single mode between an input part and an output part. Ridge type waveguides do offer improved lateral confinement of the interacting waves, but there remains an asymmetry in the vertical direction which limits the efficiency of the conversion process.
Harada et al. (U.S. Pat. No. 4,952,013) teach the formation of an optical wavelength conversion device of an optical fiber configuration, wherein the fiber has a core of nonlinear material and a cladding of amorphous material with a lower index of refraction than the core. The conversion is carried out by a method of Cherenkov radiation (see Umegaki, cited above) in which phase matching is carried out between the fundamental mode propagating in the core and a second harmonic mode propagating within the cladding.
Using the currently more conventional QPM phasematching in domain reversed crystalline material, Matsuda et al. (U.S. Pat. No. 5,313,543) provide a second harmonic generation device in which a waveguide layer passes through a region of domain reversals in a ferroelectric crystal. Within the objects of the method there is a primary object of reducing the noise inherent in the fundamental wave resulting from reflections of the fundamental wave from an inlet of the waveguide.
Okazaki et al. (U.S. Pat. No. 5,436,757) provide an optical wavelength converting apparatus wherein two laser inputs can provide fundamental waves of different wavelengths and a nonlinear ferroelectric conversion device can combine the input waves in various sum and difference combinations.
Hatori (U.S. Pat. No. 6,195,198 B1) provides an optical frequency doubling ferroelectric device which includes a waveguide formed therein and a laser input source incorporating a beam-splitter/mirror to reflect a portion of the input wave back to the laser. The reflected portion passes through a narrow band-pass filter and is used to lock the oscillation frequency of the laser.
Yamamoto et al. (U.S. Pat. No. 5,515,471) teach the formation of a frequency doubler comprising a ferroelectric crystal within which periodic inverted domain regions have been formed by proton exchange followed by a heat treatment. A waveguide region is also formed within the crystal, passing through the regions of domain inversion.
Within the method, a nonlinear degradation layer is formed on the surface of the waveguide, wherein the TM00 mode within the waveguide is converted to a TM10 mode which is then frequency doubled by passage through the crystal.
As was noted above, a major factor in producing wave confinement within a waveguide region is the symmetry of the index of refraction within the region, particularly with respect to the vertical direction from the surface of the crystal to the interior of the crystal. In most of the prior art, the waveguide region is formed within the crystal by subjecting a region below the crystal surface to proton exchange in order to change the index of refraction of that region. This process generally involves the diffusion of a proton exchange medium (eg. benzoic acid) through patterned openings in the crystal surface and thereafter into the crystal interior. The diffusion process is typically enhanced by a subsequent heat treatment of the crystal that produces an equilibrium between diffusion caused by gradients in chemical concentration and diffusion caused by temperature gradients. As has been discussed above, these processes take a long time and can cause significant damage to the crystal, particularly to its surface. In addition, the symmetry that is obtained for the index of refraction within the waveguide region, particularly that portion of the waveguide region adjacent to the crystal surface, is often less than adequate for the efficient conversion process. The purpose of the present invention, therefore, is to provide a method of producing a waveguide region buried within a ferroelectric crystal that is characterized by a symmetric index of refraction and yet has a processing time of reasonable length and does not damage the crystal surface.